Abstract
Encouraged by the global agreement between theoretical predictions and experimental measurements for $B \to J/\psi V$ decays, we extend that perturbative QCD formalism to $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays at the presently known next-to-leading order in the quark-antiquark description of $f_0(500)$ and $f_0(980)$. With the angle $\phi_f \approx 25^\circ$ of the $f_0(500)-f_0(980)$ mixing in the quark-flavor basis, we find that the branching ratios of the $B_d^0 \to J/\psi f_0(500) (\to \pi^+ \pi^-)$ and $B_{d,s}^0 \to J/\psi f_0(980) (\to \pi^+ \pi^-)$ modes generally agree with the current data or the upper limits within uncertainties, except for the seemingly challenging $B_s^0 \to J/\psi f_0(500) (\to \pi^+\pi^-)$ one. Then, we further explore the relevant observables of the $B_{d,s}^0 \to J/\psi f_0(500) [f_0(980)]$ decays, which could provide further constraints on the mixing angle $\phi_f$ and/or SU(3) flavor symmetry breaking effects. As a byproduct, we predict ${\rm BR}(B_{d}^0 \to J/\psi f_0(980)(\to K^+ K^-))=5.8^{+3.1}_{-2.9} \times 10^{-7}$ and ${\rm BR}(B_{s}^0 \to J/\psi f_0(980)(\to K^+ K^-)) =4.6^{+2.6}_{-2.3} \times 10^{-5}$. All theoretical predictions await the future examinations with high precision.
Highlights
It is well known that the golden modes B0d → J=ψKS and B0s → J=ψφ in the heavy b flavor sector provide an ideal ground to test the standard model(SM) and search for the possible new physics beyond SM
Note that the significant nonzero deviations experimentally to the SM predictions for the interesting sin φd and sin φs would indicate the exotic new physics beyond SM, and especially the latter one is of great interest
Encouraged by the global agreement between the data and the theoretical predictions in the perturbative QCD (PQCD) approach [36,37,38,39] on the B → J=ψV decays at the nextto-leading order (NLO) accuracy [40], we extend that formalism to the B0d;s → J=ψσðf0Þ decays in the quarkantiquark description of σ and f0 with including the known NLO corrections in αs, namely, the vertex corrections
Summary
It is well known that the golden modes B0d → J=ψKS and B0s → J=ψφ in the heavy b flavor sector provide an ideal ground to test the standard model(SM) and search for the possible new physics beyond SM. (d) Under the assumption of two-quark structure and the σ − f0 mixing, Li et al studied the B0s → J=ψσðf0Þ decays with a mixed “QCD factorization plus perturbative QCD (PQCD) factorization” approach [29] and predicted the branching ratios BRðB0s → J=ψ f0Þ 1⁄4 2.43þ−00..3310 × 10−4 and BRðB0s → J=ψσÞ 1⁄4 4.72þ−00..5692 × 10−5, corresponding to the mixing angle φf about Æ34°. With the perturbative calculations of both tree and penguin amplitudes in the PQCD approach, we could provide the predictions on the observables such as the CP-averaged branching ratios, the CP-violating asymmetries, and so forth with much more reliability These reliable calculations would help us to further investigate the impact of the penguin contributions to the CP asymmetry measurements, even the extraction of weak phases φd;s, and explore the useful information such as the mixing angle φf between the mixtures of σ and f0, if they are really the qqmesons. The related weak effective Hamiltonian Heff for the B0dðsÞ → J=ψfqðsÞ decays mentioned above can be written as [55]
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